All that this means is that one company is owned and controlled by the other company. If Company A is a subsidiary of Company B, then Company B holds the majority of the voting stock in Company A and can control Company A's operations. As an example of this in the US, the Time-Warner corporation has subsidiaries such as CNN and HBO.
It is very common for companies to have subsidiaries or to be the subsidiary of another company. One major reason for this is so that the parent company can have many sources of income without becoming too centralized. The parent company can benefit financially but can still allow the subsidiaries to have their own management teams that are expert in their particular area. Such subsidiaries are also easier to sell if that becomes appropriate.
A subsidiary can be described as a company own by another company. Once a company has more than 51% ownership of another company it becomes it subsidiary